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%I #11 Feb 28 2023 09:46:38
%S 1,1,1,1,2,4,1,3,9,9,1,4,16,24,36,1,5,25,50,100,100,1,6,36,90,225,300,
%T 400,1,7,49,147,441,735,1225,1225,1,8,64,224,784,1568,3136,3920,4900,
%U 1,9,81,324,1296,3024,7056,10584,15876,15876,1,10,100,450,2025,5400,14400,25200,44100,52920,63504
%N Triangle read by rows. T(n, k) = binomial(n, ceil(k/2)) * binomial(n, floor(k/2)).
%e Triangle T(n, k) starts:
%e [0] 1;
%e [1] 1, 1;
%e [2] 1, 2, 4;
%e [3] 1, 3, 9, 9;
%e [4] 1, 4, 16, 24, 36;
%e [5] 1, 5, 25, 50, 100, 100;
%e [6] 1, 6, 36, 90, 225, 300, 400;
%e [7] 1, 7, 49, 147, 441, 735, 1225, 1225;
%e [8] 1, 8, 64, 224, 784, 1568, 3136, 3920, 4900;
%e [9] 1, 9, 81, 324, 1296, 3024, 7056, 10584, 15876, 15876;
%p A360859 := (n, k) -> binomial(n, ceil(k/2)) * binomial(n, floor(k/2)):
%p seq(seq(A360859(n, k), k = 0..n), n = 0..10);
%o (Python)
%o from math import comb
%o def A360859_T(n,k): return comb(n,m:=k>>1)**2*(n-m)//(m+1) if k&1 else comb(n,k>>1)**2 # _Chai Wah Wu_, Feb 28 2023
%Y Cf. A018224 (main diagonal), A360861 (row sums).
%Y Cf. A360857, A360858.
%K nonn,tabl
%O 0,5
%A _Peter Luschny_, Feb 28 2023
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